Minimum-Error Probabilities in Demodulation of Binary PCM Signals

For ordinary binary PCM waveforms, the minimum-error probability demodulation operation is determined when decisions are made one-word-at-a-time utilizing an arbitrary number, n, of statistically dependent, received, noisy words. A method is then developed for simulating the minimum-error demodulation with a digital computer for the case of additive white Gaussian noise. By a Monte Carlo technique, minimum-error probabilities are computed for Gaussian data for n = 2 and n = 1, and for 3-bit and 6-bit words. The results are applicable regardless of the waveforms used to represent the binary digits (or bits). These results indicate that for word-error probabilities less than about 0.1, no very significant power gains accrue from the use of statistical dependence in the data unless the correlation coefficients between data samples are large (i.e., 0.98 or greater) for a large number of transmitted samples. However, the results also indicate that the effect of using the statistical dependence in the data is to reduce errors in the high order (most significant) bits of the code. Hence, significant gains might be obtained if an error amplitude criterion were used rather than error probability.